As his deputy headed to the White House last week to handle a high-profile confrontation over an FBI informant, Attorney General Jeff Sessions was en route to a law-enforcement summit in Bulgaria, followed by meetings with the prime minister to talk about terrorism and border security.

A few days later, when Deputy Attorney General Rod Rosensteinhosted an unusual follow-up briefing for lawmakers to discuss intelligence material on the informant, Mr. Sessions was meeting with the interior minister of Croatia about Justice Department...